Question

1. A statistician is interested in the gross earnings of several of her favorite bands. She took a random sample of

30 of the Rolling Stones’ North American concerts, and found that the gross earnings averaged $2.27 million

with a standard deviation of $0.5 million. One source suggests that the average gross earnings per concert for

every stadium performance in North America is $2.11 million. Do the Rolling Stones earn more on average?

Test at a 5% level of significance

2. A survey was conducted about the cost for a family of four to visit an amusement park for one day. A sample

of 32 families yielded an average cost of $190.28 with a standard deviation of $51.75. Last year, a magazine

published that the average cost for a family of four to visit an amusement park was $175. Based on the sample

data above, can we conclude that the mean cost is actually higher than this at α=.05

3. According to a large local high school, senior students have a mean GPA of 3.07. A random sample of 38

seniors taking AP courses showed a mean GPA of 3.29 with a standard deviation of 0.42. At the 1% level of

significance, can it be stated that seniors taking AP courses have a different GPA than the senior class as a

whole?

Answer 1

1)

Answer)

Null hypothesis Ho : u = 2.11

Alternate hypothesis Ha : u > 2.11

As the population standard deviation is unknown here we will use t distribution table to conduct the test

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (2.27 - 2.11)/(0.5/√30) = 1.75

From z table, P(z>1.75) = 0.0401

P-value = 0.0401

As the obtained p-value is less than 0.05, given significance

We reject the null hypothesis Ho

We have enough evidence to conclude that u > 2.11